Autocatalytic networks with intermediates I: Irreversible reactions

A class of autocatalytic reaction networks based on template-dependent replication and specific catalysis is considered. Trimolecular “elementary steps” of simple replicator dynamics are resolved into two consecutive irreversible reactions. The extreme cases, competition for common resources and hypercycle-like cooperative feedback, were analyzed in some detail. Although the dynamics of the extended networks resembles corresponding replicator dynamics in general, there are significant differences. Most notably, the interior fixed points in the cooperative model turned out to be asymptotically stable for an arbitrary number of species, whereas simple replicator dynamic predicts an asymptotically stable periodic orbit fixed for four species and fewer and a stable periodic orbit for all other cases.